Heat the oil in a large saucepan over medium-high heat. Add the ginger, garlic, and scallion whites and cook, stirring frequently, until softened, 2 to 3 minutes. Stir in the curry powder. Add the carrots, potato, lentils, broth, ¾ teaspoon salt, and ¼ teaspoon pepper. Bring to a boil, reduce heat, and simmer, stirring occasionally, until the lentils and vegetables are tender, 15 to 20 minutes.
Sprinkle the curry with the scallion greens and serve with the naan and lime wedges.